Instead of minimizing the amount of money Tudor pays, we will rephrase the problem as trying to maximize the amount of money Tudor saves, as the total cost of the $N$ cheeses with no discounts is by definition equal to the amount of money Tudor actually pays plus the amount of money he saves.

If we rephrase the problem in this way, then the problem actually reads as follows - we have $N$ integers and want to compute the sum of the $K$ largest ones. The most obvious way to do this is to use an $\mathcal{O}(N\log N)$ sorting algorithm, which comfortably runs in time.

This can also be done in linear time, though that was not necessary for this problem.